Sparsification of Monotone $k$-Submodular Functions of Low Curvature

TL;DR

This paper introduces an efficient sparsification algorithm for monotone $k$-submodular functions with low curvature, expanding the scope of sparsification techniques beyond graphs and hypergraphs.

Contribution

It extends previous work by Rafiey and Yoshida, providing a novel sparsification method specifically for monotone $k$-submodular functions of low curvature.

Findings

Developed an efficient sparsification algorithm.

Applicable to a broader class of functions.

Potential for improved computational efficiency.

Abstract

Pioneered by Benczur and Karger for cuts in graphs [STOC'96], sparsification is a fundamental topic with wide-ranging applications that has been studied, e.g., for graphs and hypergraphs, in a combinatorial and a spectral setting, and with additive and multiplicate error bounds. Rafiey and Yoshida recently considered sparsification of decomposable submodular functions [AAAI'22]. We extend their work by presenting an efficient algorithm for a sparsifier for monotone $k$-submodular functions of low curvature.